Electrical characteristics associated with a filament resistance are detected to control a preheating amount so as to heat a filament into an optimum state for emission in accordance with determined preheating time. A ballast for a discharge lamp includes an inverter including at least one or more switching elements connected to an output end of a DC power source, a control circuit or controlling switching in the inverter, a resonant circuit connectable to a discharge lamp with a thermionic cathode, a load circuit connected to an output end of the inverter, a preheating circuit for preheating a filament of the discharge lamp, and a detection circuit for detecting electrical characteristics associated with a filament resistance of the discharge lamp. The electrical characteristics associated with a filament resistance are detected by the detection circuit to control a preheating amount for the filament, in accordance with a filament resistance value and determined preheating time, so that a ratio of a hot resistance Rh to a cold resistance Rc in the filament falls in a range of 4.0 or more and less than 5.5.